Answer:
a) 25.15
b)
x = 1
y = t
z = (4pi)^2 + t *(8pi) = 4pi(4pi + 2t)
c) (x,y) = (1, -2pi)
Step-by-step explanation:
a)
First lets calculate the velocity, that is, the derivative of c(t) with respect to t:
v(t) = (-sin(t), cos(t), 2t)
The velocity at t0=4pi is:
v(4pi) = (0, 1, 8pi)
And the speed will be:
s(4pi) = √(0^2+1^2+ (8pi)^2) = 25.15
b)
The tangent line to c(t) at t0 = 4pi has the parametric form:
(x,y,z) = c(4pi) + t*v(4pi)
Since
c(4pi) = (1, 0, (4pi)^2)
The tangent curve has the following components:
x = 1
y = t
z = (4pi)^2 + t *(8pi) = 4pi(4pi + 2t)
c)
The intersection with the xy plane will occurr when z = 0
This happens at:
t1 = -2pi
Therefore, the intersection will occur at:
(x,y) = (1, -2pi)
Answer:
X is 36 and y is 48.
Step-by-step explanation:
So a couple of things here: both triangles are equal, and triangles always add up to 180 degrees. If we do some math:
180-108-48=24
This means that 2x-y needs to equal 24. We know what y is, it's 48 since both triangles are equal. Lets do some more math to find x.
48+24=72
72 divided by 2 = 36. 36 is the answer for x.
Answer:
j=42
Step-by-step explanation:
since it's 7x larger you just have to multiple 6 by 7 to find j
20X0.3= 6
30X0.3= 9
40X0.3= 12
A line. It goes in both directions forever
